(19)
(11) EP 2 867 705 B1

(12) EUROPEAN PATENT SPECIFICATION

(45) Mention of the grant of the patent:
21.09.2022 Bulletin 2022/38

(21) Application number: 13717836.4

(22) Date of filing: 11.04.2013
(51) International Patent Classification (IPC): 
G01V 1/30(2006.01)
(52) Cooperative Patent Classification (CPC):
G01V 1/30; G01V 2210/643; G01V 2210/641
(86) International application number:
PCT/GB2013/050941
(87) International publication number:
WO 2014/001751 (03.01.2014 Gazette 2014/01)

(54)

ADAPTIVE HORIZON TRACKING

ADAPTIVE HORIZONTVERFOLGUNG

SUIVI ADAPTATIF D'HORIZON


(84) Designated Contracting States:
AL AT BE BG CH CY CZ DE DK EE ES FI FR GB GR HR HU IE IS IT LI LT LU LV MC MK MT NL NO PL PT RO RS SE SI SK SM TR

(30) Priority: 29.06.2012 GB 201211603

(43) Date of publication of application:
06.05.2015 Bulletin 2015/19

(73) Proprietor: Foster Findlay Associates Limited
Tyne and Wear NE1 2LA (GB)

(72) Inventors:
  • PURVES, Steven
    Tyne and Wear NE25 9NN (GB)
  • LOWELL, James
    Durham DH7 0EB (GB)
  • NORTON, Dale
    Oldham, Lancashire OL4 2NE (GB)
  • HENDERSON, Jonathon
    Northumberland NE61 8PL (GB)

(74) Representative: HGF 
HGF Limited 1 City Walk
Leeds LS11 9DX
Leeds LS11 9DX (GB)


(56) References cited: : 
WO-A2-02/03099
US-A1- 2004 260 476
US-A- 5 056 066
   
  • Nicholas Mcardle ET AL: "Advanced Multiattribute Imaging and Geobody Delineation of Jurassic and Triassic Stratigraphic Targets", GCSSEPM 2011, 1 December 2011 (2011-12-01), pages 230-250, XP055102398, Retrieved from the Internet: URL:http://www.ffa-geosciences.com/downloa d/GCSSEPM_2011_Multiattribute.pdf [retrieved on 2014-02-14]
  • GAYNOR PATON ET AL: "Adaptive geobodies: delineation of complex and heterogeneous stratigraphic features", ANNUAL INTERNATIONAL SEG MEETING, XX, XX, 1 January 2011 (2011-01-01), pages 4384-4387, XP002718976,
  • Jonathan Henderson: "Geological Expression: data driven-interpreter guided approach to seismic interpretation", First Break, 1 March 2012 (2012-03-01), pages 73-78, XP055102400, Retrieved from the Internet: URL:http://www.ffa-geosciences.com/downloa d/FirstBreakMarch2012.pdf [retrieved on 2014-02-14]
  • NIKOS PARAGIOS ET AL: "Geodesic Active Regions: A new framework to deal with frame partition problems in Computer Vision", JOURNAL OF VISUAL COMMUNICATION AND IMAGE REPRESENTATION, ACADEMIC PRESS, INC, US, vol. 13, no. 1-2, 30 March 2002 (2002-03-30), pages 249-267, XP002671835, ISSN: 1047-3203, DOI: 10.1006/JVCI.2001.0475 [retrieved on 2002-03-25]
  • Shin-yee Lu ET AL: "An iterative approach to seismic skeletonization", GEOPHYSICS, vol. 55, no. 10, 1 October 1990 (1990-10-01), pages 1312-1320, XP055613628, US ISSN: 0016-8033, DOI: 10.1190/1.1442778
   
Note: Within nine months from the publication of the mention of the grant of the European patent, any person may give notice to the European Patent Office of opposition to the European patent granted. Notice of opposition shall be filed in a written reasoned statement. It shall not be deemed to have been filed until the opposition fee has been paid. (Art. 99(1) European Patent Convention).


Description


[0001] The present invention relates generally to the field of oil and gas exploration, and in particular to the field of computer aided exploration for hydrocarbons using geophysical data, such as for example seismic data, of the Earth. In particular, the present invention relates to a computerized method for adaptively determining and visualizing (modelling) geological objects, such as horizons, in a volume of representative geophysical survey data.

Introduction



[0002] In the oil and gas industry, geological data surveys such as, for example, seismic prospecting and other similar techniques are commonly used to aid in the search for and evaluation of subterranean hydrocarbon deposits. As an example, prospecting operations include three basic stages (i) data acquisition, (ii) data processing and (iii) data interpretation. The success of the prospecting operation generally depends on satisfactory completion of stages (i), (ii) and (iii). For example, a seismic source is used to generate an acoustic signal that propagates into the Earth and that is at least partially reflected by subsurface seismic reflectors, also known as horizons. The reflected signals are then detected and recorded by an array of seismic receivers located at or near the surface of the Earth, in an overlying body of water, or at known depths of boreholes. Jonathan Henderson in "Geological Expression: data driven-interpreter guided approach to seismic interpretation",First Break, 1 March 2012 (2012-03-01), pages 73-78, employs multiple forces to control the growth of a geobody.The mesh and geobody delineation process is initialized by selection of one or more internal and external seed points. The forces controlling the growth are based on the local image gradient, a comparison of the seed point statistics, and the statistics of the data around the current mesh point and a surface elasticity constraint. Each node on the surface mesh moves as directed by the resultant of all these forces until an equilibrium state is achieved.

[0003] Figure 1 shows a typical setup for offshore seismic surveys, where a large seismic survey vessel 10 is used to tow acoustic receivers 12, also known as streamers, suspended below the surface, which carry hydrophones (not shown). During data acquisition, sound waves 14 are transmitted from the vessel 10 using compressed air guns 16 which travel down through the seabed and reflect back from the different layers of rock 18, 20, 22 in the subsurface (i.e. horizons). The reflected sound waves 14 are then received by the hydrophones (not shown) located along the seismic streamers which when processed can be used to provide a visual representation (2D, 3D) of the substrata.

[0004] Typical seismic traces of the reflections (amplitudes) are shown in Figure 2. The data shown in Figure 2 has been migrated, i.e. the amplitudes of the traces are moved to their true subsurface position (depth) to eliminate any offset.

[0005] Figures 3 and 4 show an example of a 3D seismic data volume 24 and a respective 2D slice 26 of the 3D seismic volume 24 based on the migrated reflectivity data. The representation clearly shows different horizons 28 and allows the identification of faults. In the field of geology, a horizon is defined as an interface surface separating two strata having different properties or of different composition.

[0006] In reflection seismology, a horizon may also have a broader meaning relating to any change in acoustic properties which can be mapped as a geological surface or a natural contour underlying the data. As such, a given interpreted horizon may be expressed within the data in different ways depending on the geological nature of the surface (i.e. the rock and fluid properties at the interface of two strata, presence of an unconformity surface) and on imaging and data processing parameters (i.e. phase correction applied to the data).

[0007] The result is that a horizon may be tracked on any natural contour that is apparent and differentiatable within the seismic data, not only the amplitude peaks or troughs evident in Figure 2.

[0008] In the field of geology, faults 30 are surfaces within the Earth's crust at which sedimentary reflective layers (e.g. strata and horizons) and other geological features are disrupted. In particular, faults 30, which often continue through multiple horizon layers 28, can form effective barriers to subsurface hydrocarbon flow, causing oil and gas to accumulate at such horizon 28 / fault 30 intersections.

[0009] Accordingly, the precise detection and characterization of individual horizon layers 28 and the faults 30 disrupting such horizons 28 is a very important tool in the search for oil and gas reserves, and the accuracy and completeness with which these so called geological objects (e.g. horizon, fault) can be detected and characterized may have a significant impact on identifying and exploiting those reserves.

[0010] However, the interpretation of the vast geological data accumulated in, for example, 3D seismic data surveys, is a very time-consuming task that currently requires advanced interpretation workstations and trained experienced personnel, such as an experienced geophysicist (i.e. a seismic interpreter). Therefore, it is today's common practice to use automated techniques, semi-automated and fully automated horizon tracker software systems in order to process the amount of data produced by modern geological surveys. However, the known automated techniques and available horizon trackers typically generate the tracked horizon along orthogonal grid axes and are relatively limited when trying to accurately follow the topological changes of the true reflective horizon, or when combining a tracked reflective surface that started from multiple seeds planted within the region of interest.

[0011] In particular, conventional horizon trackers commonly fail to follow a desired seismic event (i.e. reflective surface, horizon) due to poor quality data, causing discontinuities within the data (non-continuous data), event dimming or chaotic faulted areas. Such poor quality data can cause these horizon trackers to jump between different reflective horizons and subsequently follow a wrong event.

[0012] Typical causes for such discontinuities within the data representing a reflective horizon may be: (i) physical breaks in the reflective horizon; (ii) changes in rock type or geometry, causing fluctuations in material properties (e.g. density, elastic moduli) and changes in impedance, which may further result in brightening or dimming of the visual representation of the data; (iii) variation in layering and layer thicknesses at and around seismic resolution causing tuning effects and the horizon becoming unresolved (iv) signal attenuation caused by adjacent reflective layers or faults; (v) localized high or low velocity zones, causing "pull-ups"/"sags" in the reflective horizon; (vi) interference with neighbouring layers at converging/diverging zones; (vii) acquisition noise, usually a coherent noise with a very linear footprint that is aligned with the survey grid (snail lines), and (viii) processing noise, such as hyperbolic noise, which is coherent and an artefact of migration.

[0013] In addition, many conventional horizon trackers fail to automatically "cross" barriers, such as physical breaks in the horizon caused by faulting or fracturing, so that additional seeds have to be placed manually by the operator, in order to generate a computer model of correlating reflective surfaces (i.e. horizon) throughout the entire 3D seismic data volume.

[0014] Accordingly, it is an object of the present invention to provide a method and an improved workflow for adaptive horizon tracking. In particular, it is an object of the present invention to provide improved computer executable algorithms adapted to generate and evolve a more accurate computer model of the natural contour of a reflective surface (i.e. horizon) from at least one seed point irrespective of disruptions caused by faults or discontinuities caused by "poor" data.

Summary of the Invention



[0015] The computer-implemented algorithm as defined in claim 1 and the method as defined in claim 11 solve the aforementioned problems. Preferred embodiments are defined in the dependent claims.

[0016] According to an aspect of the present invention, there is provided a computer-implemented algorithm adapted to propagate a boundary surface of a seed that is placed within a first region of interest of a visual representation of a 3D seismic data so as to follow a probable contour of a discontinuous data representation of at least part of said first region of interest, wherein said algorithm is executable to:

generate at least one characteristic parameter for a plurality of candidate events of said 3D seismic data within a predefined gate region located forward of said propagating boundary surface;

generate and assign a probability characteristic for said plurality of candidate events based on said at least one characteristic parameter;

determine a plurality of events of at least part of at least a second region of interest located substantially parallel to and conformant with at least part of said first region of interest; and

propagate said boundary surface through said non-continuous data representation utilizing a link between said propagating boundary surface and said plurality of events of at least part of said at least one second region of interest. Advantageously, the computer executable algorithm is further executable to generate at least one attribute volume comprising at least one attribute derivable from said 3D seismic data.



[0017] In the invention, the link is provided by at least one constraint defined in accordance with said probability characteristics assigned to each one of said plurality of candidate events of at least part of said first region of interest. Further in the invention, the at least one constraint is adapted to provide an internal force between respective events of at least part of said first region of interest and at least part of said at least one second region of interest. In the invention, the internal force between respective events may be inversely proportional to said probability characteristics of each one of said plurality of events of at least part of said first region of interest.

[0018] This provides the advantage that regions of poor quality data can be "crossed" using a conformant guide reflector (i.e. a parallel reflective surface) to steer the propagating boundary surface along a most likely contour of the tracked reflective surface. In particular, the "weak" events are linked to the guide reflector using constraints that are dependent on the actual "weakness" of each event, i.e. the weaker the event, the stronger the link to the guide reflector and vice versa. This ensures that the most likely model of the reflector surface of the region of interest (horizon) is generated through the entire 3D seismic volume.

[0019] The computer executable algorithm may further be executable to generate at least one attribute volume comprising at least on attribute derivable from said 3D seismic data This provides the advantage of an improved selectability of candidate events allowing the computer model to more closely follow the natural contour of the tracked reflective surface.

[0020] Advantageously, the constraint may include a selectively adjustable weighing factor. This provides the advantage that the operator can manually adjust the boundary conditions of the guide reflector in order to selectively steer the computer model along the most likely contour of the tracked reflective surface.

[0021] According to a second aspect of the present invention, there is provided a computer executable algorithm adapted to propagate a boundary surface of a seed that is placed within a first region of interest of a visual representation of a 3D seismic data so as to follow a natural contour of a data representation of at least part of said first region of interest, wherein said algorithm is executable to:

generate and assign a probability characteristic for a plurality of candidate events within a predefined gate region located forward of said propagating boundary surface;

generate an optimization function based on said probability characteristic of each one of said plurality of candidate events;

deform and propagate said boundary surface in accordance with said optimization function.



[0022] Advantageously, the optimization function may be a cost function field adapted to provide an external force function within said predefined gate region. Even more advantageously, the predefined gate region may be a predefined region forward of said propagating boundary surface. Preferably, the predefined gate region may be selectively adjustable.

[0023] This provides the advantage that by using optimization functions, such as cost functions, to propagate the boundary surface of the computer model of the tracked reflective surface (horizon), the boundary surface can evolve naturally in very small steps depending on a predefined acceptance criteria allowing the natural contour of the reflective surface to be tracked very accurately. In addition, any barriers (i.e. faults, discontinuities etc.) can be "crossed" utilizing, for example, attractors that are provided by the cost function for each one of the candidate events. For example, candidate events of the tracked reflective surface may be determined on either side of such a barrier. The resulting cost values for each one of the candidate events can then be used to generate an attractive force towards the propagating boundary surface, allowing the boundary surface of the generated computer model to move across any barrier within the gate region and continue tracking the natural contour of the reflective surface without any intervention from the operator.

[0024] According to a third aspect of the present invention, there is provided a method for adaptively determining one or more horizons from 3D seismic data, comprising the steps of:

generating at least one attribute volume comprising a plurality of attributes from said geological survey data;

identifying at least one region of interest on a predetermined cross-section of said at least one attribute volume;

adding at least one seed to said at least one region of interest;

defining at least one representative area in accordance with said region of interest;

generating a geological object applying a computer executable algorithm according to the first aspect of the present invention and/or the second aspect of the present invention;

monitoring a visual representation of said geological object during generation; selectively stopping said generation of said geological object;

generating an optimized geological object through manipulation of at least part of said geological object.



[0025] The new workflow of the present invention provides several advantages. In particular, being able to apply any combination of or all of the computer executable algorithms of the first, second and third aspects of the present invention provides an extremely high adaptability to varying data quality, quantity and/or varying boundary conditions, allowing the tracking of a natural contour of a reflective surface at maximum accuracy and most effectively. In addition, the capability of having an attribute volume comprising more than one attribute can further improve the detectability / identifyability of a geological object (e.g. a horizon or fault) due to an optimized view of stratigraphic features. In addition, manual and/or automated manipulation of the geological object while it is generated and/or adapted (i.e. real-time visual inspection and feedback of the "growing" feature) by the system, allows for much faster interpretation and optimization of the feature of interest when compared to conventional techniques.

[0026] Furthermore, by defining at least one representative area in addition to a seed placed in the region of interest further improves the quality of input information provided to the system, making the method more robust to any changes of the characteristics of the feature of interest and therefore allowing a wider variety of geological features, to be tracked. For example, the operator, such as an experienced interpreter, may select a reflective surface (horizon) and draw a seed along at least part of the feature's length so that it can be adapted (i.e. "grown") into a computer model surface representation of the horizon within the attribute volume. The operator may further select additional areas of the reflective surface of interest providing the system with further qualitative input when adapting the seed. Also, the method allows inputting qualitative information to the system from representative areas of one or more separate, but corresponding horizon features.

[0027] Advantageously, the attribute volume may be generated from seismic attributes determined from said 3D seismic data. In the third aspect of the invention, the region of interest may comprise of at least one horizon. Typically, the at least one representative area may be an area that is part of said at least one horizon or an area that may not be part of said at least one horizon. Alternatively, at least one first representative area may be an area that is part of said at least one horizon and at least one second representative area may be an area that may not be part of said at least one horizon.

[0028] Steps (c) to (e) of the method of the third aspect of the present invention may be repeated until an acceptance criteria is satisfied. Advantageously, the generation of said at least one optimized geological object in step (h) of the method of the third aspect of the present invention may be achieved through manual manipulation and/or through automatic manipulation in accordance with said at least one predetermined constraint. Preferably, steps (f) to (h) of the method of the third aspect of the present invention may be repeated after adding at least one additional seed and/or defining at least one additional representative area and/or manually manipulating the geological object. Even more preferably, the manual manipulation may include any one of point-by-point editing, surface stretching, segment joining and segment splitting.

[0029] This provides the advantage that further qualitative information can selectively be input to the system further improving the adaption / generation of the reflective surface of interest allowing the operator to guide the system along the natural contour of the reflective surface.

[0030] Advantageously, the seed and/or representative area may be defined by any one of a point, a line defined by a plurality of points, a polygon defined by a plurality of points, an image mask selected from said attribute volume and an area or region painted in said region of interest. The at least one attribute volume may be a plurality of attribute volumes, each determined from predetermined characteristic attributes of said geological data.

[0031] Advantageously, the at least one dataset of said at least one optimized geological object may be exportable for further processing.

[0032] According to a fourth aspect of the present invention, there is provided a computer system for adaptively determining one or more horizons from geological data obtained by a method according to the method of the third aspect of the present invention, comprising a computer readable memory for storing data, an output device, a computer processor and an input device, such as a man-machine interface adapted to enable an operator to operate the system.

[0033] According to a fifth aspect of the present invention, there is provided a computerreadable storage medium having embodied thereon a computer program, when executed by a computer processor, that is configured to perform the method of any one of the first aspect of the present invention and/or the second aspect of the present invention and/or the third aspect of the present invention.

Brief Description of the Drawings



[0034] Preferred embodiments of the present invention will now be described, by way of example only and not in any limitative sense, with reference to the accompanying drawings, in which:

Figure 1 shows a typical setup for an offshore seismic survey using an array of acoustic receivers (i.e. hydrophones) and sound waves generated by an air gun;

Figure 2 shows a typical plot of migrated reflection traces recorded by the acoustic receivers after activating the air gun;

Figure 3 shows a 3D volume of the migrated reflection data recorded by the acoustic receivers;

Figure 4 shows a 2D slice of the 3D volume shown in Figure 3 clearly showing different horizon layers;

Figure 5 shows an illustration of a propagating front of the horizon as two 2D surfaces which are close to merging, candidate events that have been selected are shown in black;

Figure 6 is an illustration of a gate region forward of its propagating boundary surface;

Figure 7 shows an illustration of a candidate event about to be selected by the advancing boundary surface;

Figure 8 shows a close-up of a section of seismic data in order to show the shape and variations between the individual waveforms;

Figure 9 shows a typical 2D slice of a 3D seismic data volume including a "weak" event region (i.e. data discontinuities);

Figure 10 shows an illustration of the link between the "weak" reflective surface of the tracked horizon and a guide surface using spring forces between respective events;

Figure 11 shows a most likely contour of the tracked horizon through the "weak" event region of Figure 9;

Figure 12 shows an illustration of cost values provided for each one of the candidate events in the gate region and vectors representing attractive forces generated from the cost values and acting on the boundary surface;

Figure 13 shows a flow diagram of a workflow of the present invention, and

Figure 14 shows a simple example of a workstation suitable for use with the present invention.


Detailed description of the preferred embodiment(s)



[0035] The exemplary embodiments of this invention will be described in relation to interpretation of 3D seismic data. However, it should be appreciated that, in general, the system and method of this invention will work equally well for any other type of 3D data from any environment.

[0036] For the purposes of explanation, it should be appreciated that the terms 'determine', 'calculate' and 'compute', and variations thereof, as used herein are used interchangeably and include any type of methodology, process, mathematical operation or technique, including those performed by a computer system 400, as depicted in a simplified form in Figure 14. The terms 'generating', 'evolving' and 'adapting' are also used interchangeably describing any type of computer modelling technique for visual representation of a subterranean environment from geological survey data, such as 3D seismic data. The terms 'tracking' and 'following' are used interchangeably with the same meaning. A 'natural contour' of a horizon is understood to be the true outline of the reflective surface of the same subterranean layer that is tracked. For example, movement between the Earth's tectonic plates may vertically offset parts of the same subterranean layer (i.e. having the same acoustic, optical or electromagnetic properties) creating a fault. The 'natural contour' of the same subterranean layer includes the stepup / step-down (vertical) caused by a fault. The term 'vertical' is understood to mean vertical within a 3D seismic volume aligned in accordance with the natural position of the strata surveyed, i.e. the stratigraphic layers are substantially horizontal within that volume and a vertical direction within that volume indicates a direction towards a position within that volume that is either above or below a referenced stratigraphic layer.

Propagating algorithm of the first embodiment



[0037] Referring now to Figure 5 to 7, a first embodiment of an algorithm executable for providing a method for propagating a front (boundary surface) 100 of at least one seed that is placed within a region of interest along the natural contour of a horizon is illustrated. In this particular example, the boundary surfaces 100, 102 of two seeds are close to merging in order to create a computer model of the natural contour of a reflective surface (i.e. horizon). Grid points 104 coinciding with the tracked surface are shown as black filled circles. Black arrows 106 on the boundary surface 100 represent the propagating direction of the evolving surface 100.

[0038] In particular, the algorithm of the first embodiment utilises both local waveform and attribute data characteristics to generate a statistical model for candidate events in a predefined gated region 108. The predefined gated region 108 is selectively adjustable by the operator in order to adapt the algorithm to the individual requirements of different regions of interest. During operation, at least one attribute characteristic, as well as at least one local waveform characteristic is determined for the candidate events enclosed by the predefined gated region 108. The algorithm then applies a probability function based on the determined attribute characteristics and respective local waveform characteristics in order to determine, whether or not, a candidate event meets an acceptance criteria and can be selected to be part of the tracked horizon. If, however, a combined probability from both the attribute characteristic and waveform characteristic of a candidate event do not exceed an acceptance criteria, the algorithm can "move" vertically (i.e. select and analyse data above or below the horizontal plane of the initially tracked horizon) to a location having the next highest probability, therefore allowing the algorithm to "jump" vertically and continue following the natural contour of the same horizon. An example of such a selection process is shown in Figure 7. The predefined gated region is then moved forward with the next computational step and attribute characteristics and waveform characteristics are determined for the "new" set of candidate events within the "new" predefined gated region. Alternatively, attribute characteristics may be determined in advance for the entire data set of the 3D seismic volume creating at least one attribute data volume that is stored in a temporary storage for further processing. The attribute characteristics for the candidate events are provided from the storage and used for selecting candidate events in accordance with the acceptance criteria.

[0039] Suitable probability functions may be the Bayes Rule based classifiers, MAPI based functions or any Fuzzy membership based functions, but any other statistical classifier adapted to select a candidate event in accordance with an acceptance criteria my be used.

[0040] In an example outside the scope of the present invention, the boundary surface 100 may be propagated across the candidate events using an active contour method and/or a level set method or any specific combination of the active contour method and the level set method according to individual requirements of the data set. In particular, when evolving the boundary surface, a marching squares algorithm, or any suitable equivalent algorithm, may be used to generate a new 2D boundary surface 100 after each evolution step (i.e. computational step).

[0041] Suitable seismic attributes may be any one of coherency, similarity, variance, semblance, amplitude, curvature, azimuth and dip, but other attributes drivable from the 3D seismic data may be used to highlight the different horizons within the 3D seismic volume.

[0042] A candidate event may be defined by a local signal such as a seismic waveform 110 (see Figure 8). Locally, seismic waveforms 110 can also be interpreted as a reflector of one of more reflections from well defined interfaces in the Earth, as a response to layering in the Earth and as interference effects due to the imaging process itself. A waveform characteristic, also known as waveform classification, may be a signature found in that seismic trace. This is typically done by working with seismic trace "segments" determined by the vertical dimension 112 (see Figure 6) of the predefined gate region 108. For example, Figures 8 shows typical seismic traces 110, wherein a section 113 displays significant variation in waveform shape (i.e. peaks, troughs, zero-crossings).

[0043] A waveform characteristic or signature based on, for example, similarities or semblance allows discrimination between these individual waveforms. Waveform characterisation may be a simple cross correlation, where the zero-lag cross correlation of a candidate event (i.e. trace segment or a waveform) is computed with regards to each of the reference segments. Optionally, the cross correlation may be provided for a plurality of zero-lags in order to provide a correlation function with regards to the position on a seismic trace. Alternatively, features of the waveform(s) may be extracted using a fixed basis set. For example, a polynomial sequence may be selected as a basis set that provides some desirable properties, such as orthogonality, invariance to a time-shift, or dilation. Particular examples of such polynomials may be Chebyshev polynomials, Legendre polynomials an any other suitable orthogonal polynomials. The extent of the polynomial sequence determines the basis function for analysing the waveforms, where each reference trace segment is first projected onto each polynomial basis set in order to generate a reference feature vector. The candidate trace segment (i.e. the candidate event) is then projected onto the polynomial basis set, generating a candidate feature vector. A waveform similarity measure can then be computed from the candidate feature vector and each of the reference vectors.

Propagating algorithm of the second embodiment (using guide horizon)



[0044] A second embodiment of the present invention includes an algorithm that allows a propagating boundary surface to "steer" through "poor" data regions of the 3D seismic volume. This algorithm may be used in a horizon tracker system in combination with the algorithm of the first embodiment or as a stand-alone algorithm. "Poor" data regions may include "weak" events 114, which may be defined as event regions whose combined probability is lower than the acceptance criteria, that can not be interpreted by the algorithm or horizon tracker system, and therefore create a barrier to the propagating boundary surface 100. An example of "weak" events 114 is shown in Figure 9.

[0045] In order to allow the propagating boundary surface 100 to cross such "weak" events 114 and continue evolving the boundary surface 100 and track the same horizon, a guide reflector surface 116, such as a conformant adjacent horizon, is used to link 115 the "weak" events 114 to respective events of the guide reflector surface 116 (see Figure 10). The link 115 is a constraint, such as a spring force and/or damper, that is implemented as an internal force in order to limit the vertical movement of the propagating boundary surface 100 at each one of the "weak" events 114. The rigidity of the spring and/or damper is inversely proportional to the combined probability characteristic (attribute characteristic, waveform characteristic) of the "weak" candidate events 114. For example, candidate events with a lower probability characteristic are linked to the guide reflector surface 116 using a stiffer spring and/or damper, so as to provide less vertical freedom. An example of a tracked horizon 117 (dotted line) using a guide reflector surface 116 is shown in Figure 11. Optionally, the link 115 may include a weighing factor that is selectively adjustable, so that the operator can control the course of the propagating boundary surface 100 to a limited extent.

Propagating algorithm of the third embodiment (optimization function)



[0046] A third embodiment of the present invention is illustrated in Figure 12 and includes an algorithm that allows the propagation of a boundary surface 100 (e.g. one or more seeds) in accordance with a probability characteristic determined for candidate events 120 within a predefined gated region 122. This algorithm may be used in a horizon tracker system in combination with the algorithm of the first and/or second embodiment or as a stand-alone algorithm.

[0047] In particular, the algorithm determines a probability characteristic for each one of the candidate events 120 and generates an optimization function that is used to create a force for each one of the candidate events adapted to attract the boundary surface 100 according to a value of the probability characteristic. Preferably, the optimization function is a cost function field created with each processing step moving the boundary surface 100 towards and past candidate events 120 that fulfil an acceptance criteria, resulting in a computer representation of the tracked horizon. As a result, any barrier (e.g. fault) to the propagating boundary surface 100 may be crossed if the combined force generated for candidate events 120 located across the barrier is sufficient to pull the boundary 100 surface past the barrier. The forces generated for the candidate events within the predefined gated region also allows the boundary surface 100 to propagate across the candidate events 120 in intervals considerably smaller that the distance between individual candidate events 120.

Workflow method



[0048] Referring now to Figure 13, a flow diagram of the workflow method of the present invention is shown. The novel workflow approach is based on presenting seismic data to an operator, such as an experienced interpreter or a trained geophysicist, and a computer system is processing the data and additional input from the operator in a manner that optimizes the visualization of the subterranean strata and the modelled geological features (e.g. horizon).

[0049] In this exemplary embodiment illustrated in Figures 13, 3D seismic data is loaded into the system for processing 200. Random noise, coherent noise or any other artefacts may be removed or at least reduced from the 3D seismic data by applying a suitable noise filter and/or spatial filter.

[0050] At least one attribute is then calculated 202 in order to synthesize an appropriate image to further improve the detectability / identifyability of specific geological features (e.g. horizons) therefore making the extraction of the feature of interest possible. The attribute data may be visualized as a 2D slice from the 3D attribute volume 204. Suitable attributes of the 3D seismic data may be any one of coherency, similarity, variance, semblance, amplitude and structural attributes, such as curvature, azimuth and dip (as is known in the art), but any other attribute derivable from the geophysical data may be used to make the horizons more visible.

[0051] Optionally, a plurality of attributes may be combined and displayed using a colour blend 203 for the juxtaposed attribute values, thus, providing an improved confidence level for the shape/profile and location/orientation of the horizon.

[0052] Once the attribute volume has been generated, the operator (interpreter, trained geophysicist) initializes a new adaptive segment 206 by "planting" a seed in a region of interest (e.g. a horizon feature) and starting the adaption/generation process of the horizon from the seed. In particular, a seed is "planted" by simply drawing or picking a seed in the region of interest. A seed may be a point, a line defined by a plurality of points, a polygon defined by a plurality of points, an area painted within the region of interest or an image mask selected within the attribute volume.

[0053] One or more representative areas having the same or at least similar characteristics as the region of interest may also be defined by the operator at this stage. In particular, it is possible to provide the system with additional input for generating and adapting a horizon from other horizon regions that do not appear to be part of the region of interest, but which are easier to identify and select from the attribute volume.

[0054] Optionally, one or more excluded representative areas may be defined by the operator in order to provide further input to the system helping to "guide" the adaption of the horizon along a "true" natural contour within the attribute volume.

[0055] Additional seeds can be planted 208 within the region of interest during this stage, wherein the initialization of the adaptive segment is repeated each time a new seed is planted until the operator is satisfied with the initial shape and orientation of the horizon.

[0056] When generating and adapting 210 the horizon of interest, a basic geological object having a probability characteristic for each candidate event so that the subsequent cost function field may provide external forces that encourages propagation in a data driven manner along the natural contour of the horizon of interest and as sampled by each seed. Additionally, excluded representative areas are also used in order to limit its deformation into such regions. In particular, the open surface mesh propagation is based on internal forces providing boundary conditions that limit the open surface mesh to geological meaningful shapes, i.e. as defined / constrained by surface topological measurements, therefore preventing the horizon to evolve/adapt into pathological cases. Preferably, the open surface mesh is limited to outward "in-plane" (i.e. planar) propagation, but this limitation is not understood as an exclusion of any other suitable techniques for mesh propagation. During this process, the operator can selectively alter the deformation parameters (e.g. external forces, internal forces) and the horizon will adapt to the new parameters and interactively alter the deformation/adaption accordingly. In particular, the effect of the internal forces on the deformation process may be varied by changing an "importance" or "weighting" factor attached to the defined internal forces.

[0057] Optionally, further seeds and/or representative areas may be added 216 at this stage, wherein the horizon adaption is re-started after each new additional input.

[0058] The method of the present invention allows the operator to monitor the evolving horizon and its boundary surface characteristics in real time, and to selectively stop 214 the adaption process manually. Alternatively and/or additionally, the adaption process of the horizon may be stopped 214 automatically by the system in accordance with boundary conditions defined by the operator.

[0059] Once the initial horizon adaption is completed, the operator may manipulate 218 at least part of the horizon and its boundary surface in order to optimize the computer model so that it complies with expert knowledge of an experienced interpreter. Suitable manual manipulation of the horizon performed by the operator may include any or all of point-by-point editing, surface stretching, surface segment joining, surface segment splitting, surface smoothing and/or surface erasing.

[0060] The final optimized representation of the horizon can then be exported 220 (e.g. as a pointset) including any characterizing information 222 derivable from the modelled horizon and/or seismic attribute data for further use.

[0061] It will be appreciated by persons skilled in the art that the above embodiments have been described by way of example only and not in any limitative sense, and that various alterations and modifications are possible without departing from the scope of the invention as defined by the appended claims.


Claims

1. A computer-implemented algorithm adapted to propagate a boundary surface of a seed that is placed within a first region of interest of a visual representation of a 3D seismic data so as to follow a probable contour of a non-continuous data representation of at least part of said first region of interest, wherein said algorithm is executable to:

(i) generate at least one characteristic parameter for a plurality of candidate events of said 3D seismic data within a predefined gate region located forward of said propagating boundary surface;

(ii) generate and assign a probability characteristic for said plurality of candidate events based on said at least one characteristic parameter;

(iii) determine a plurality of events of at least part of at least a second region of interest located substantially parallel to and conformant with at least part of said first region of interest; and

(iv) propagate said boundary surface through said non-continuous data representation utilizing at least one constraint linking said propagating boundary surface and said plurality of events of at least part of said at least one second region of interest,

wherein said at least one constraint is defined in accordance with said probability characteristics assigned to each one of said plurality of candidate events of at least part of said first region of interest; and wherein said at least one constraint is further adapted to provide an internal force between respective events of at least part of said first region of interest and at least part of said at least one second region of interest; and wherein said internal force between respective events is inversely proportional to said probability characteristics of each one of said plurality of events of at least part of said first region of interest.
 
2. A computer-implemented algorithm according to claim 1, further executable to generate at least one attribute volume comprising at least one attribute derivable from said 3D seismic data.
 
3. A computer-implemented algorithm according to claim 1 or claim 2, wherein said constraint includes a selectively adjustable weighing factor.
 
4. A computer-implemented algorithm according to any one of the preceding claims, wherein said algorithm is executable to:
propagate said boundary surface towards and incorporating any one of said plurality of candidate events within said predefined gate region that fulfils an acceptance criteria of said probability characteristic so as to generate a surface along the natural contour of said first region of interest.
 
5. A computer-implemented algorithm according to any one of the preceding claims, wherein said predefined gate region is defined by constraints provided within said 3D seismic data volume.
 
6. A computer-implemented algorithm according to any one of the preceding claims, wherein said predefined gate region includes events belonging to different vertical locations within said 3D seismic data volume relative to said first region of interest.
 
7. A computer-implemented algorithm according to any one of the preceding claims, wherein a boundary surface is propagated in accordance with an active contour method and/or level set method.
 
8. A computer-implemented algorithm according to any one of the preceding claims, wherein said algorithm is executable to:

(i) generate and assign a probability characteristic for a plurality of candidate events within a predefined, selectively adjustable gate region located forward of said propagating boundary surface;

(ii) generate an optimization function based on said probability characteristic of each one of said plurality of candidate events;

(iii) deform and propagate said boundary surface in accordance with said optimization function.


 
9. A computer-implemented algorithm according to claim 8, wherein said optimization function is a cost function adapted to determine a cost value for each one of said plurality of candidate events within said predefined gate region.
 
10. A computer-implemented algorithm according to claim 8, wherein said optimization function is a cost function field adapted to provide an external force function within said predefined gate region.
 
11. A method for adaptively determining one or more horizons from 3D seismic data, comprising the steps of:

(a) generating at least one attribute volume comprising a plurality of seismic attributes determined from said geological survey data;

(b) identifying at least one region of interest, comprising at least one horizon, on a predetermined cross-section of said at least one attribute volume;

(c) adding at least one seed to said at least one region of interest;

(d) defining at least one representative area in accordance with said region of interest;

(e) generating a geological object applying a computer-implemented algorithm according to any one of the preceding claims;

(f) monitoring a visual representation of said geological object during generation;

(g) selectively stopping said generation of said geological object;

(h) generating an optimized geological object through manual and/or automatic manipulation of at least part of said geological object in accordance with at least one predetermined constraint.


 
12. A method according to claim 11, wherein at least one first representative area is an area that is part of said at least one horizon and at least one second representative area is an area that is not part of said at least one horizon.
 
13. A method according to any one of claims 11 and 12, wherein steps (c) to (e) are repeated until an acceptance criterion is satisfied.
 
14. A method according to any one of claims 11 to 13, wherein steps (f) to (h) are repeated after adding at least one additional seed and/or defining at least one additional representative area and/or manually manipulating the geological object.
 
15. A method according to any one of claims 11 to 14, wherein said at least one attribute volume is a plurality of attribute volumes, each determined from predetermined characteristic attributes of said geological data.
 


Ansprüche

1. Computerimplementierter Algorithmus, der ausgelegt ist, um eine Grenzfläche eines Seeds zu propagieren, der innerhalb einer ersten Region von Interesse einer visuellen Darstellung seismischer 3D-Daten platziert ist, um einer wahrscheinlichen Kontur einer nicht kontinuierlichen Datendarstellung mindestens eines Teils der ersten Region von Interesse zu folgen, wobei der Algorithmus ausführbar ist zum:

(i) Generieren mindestens eines charakteristischen Parameters für eine Vielzahl von Kandidatenereignissen der seismischen 3D-Daten innerhalb einer vordefinierten Gate-Region, die sich vor der propagierenden Grenzfläche befindet;

(ii) Generieren und Zuweisen einer Wahrscheinlichkeitseigenschaft für die Vielzahl von Kandidatenereignissen basierend auf dem mindestens einen charakteristischen Parameter;

(iii) Bestimmen einer Vielzahl von Ereignissen mindestens eines Teils mindestens einer zweiten Region von Interesse, die im Wesentlichen parallel zu mindestens einem Teil der ersten Region von Interesse angeordnet ist und mit diesem übereinstimmt; und

(iv) Propagieren der Grenzfläche durch die nicht-kontinuierliche Datendarstellung unter Verwendung mindestens einer Bedingung, die die propagierende Grenzfläche und die Vielzahl von Ereignissen mindestens eines Teils der mindestens einen zweiten Region von Interesse verbindet,

wobei die mindestens eine Bedingung in Übereinstimmung mit den Wahrscheinlichkeitseigenschaften definiert ist, die jedem der Vielzahl von Kandidatenereignissen mindestens eines Teils der ersten Region von Interesse zugeordnet sind; und wobei die mindestens eine Bedingung ferner ausgelegt ist, um eine innere Kraft zwischen jeweiligen Ereignissen mindestens eines Teils der ersten Region von Interesse und mindestens eines Teils der mindestens einen zweiten Region von Interesse bereitzustellen; und wobei die innere Kraft zwischen jeweiligen Ereignissen umgekehrt proportional zu den Wahrscheinlichkeitseigenschaften von jedem der Vielzahl von Ereignissen von mindestens einem Teil der ersten Region von Interesse ist.
 
2. Computerimplementierter Algorithmus nach Anspruch 1, der ferner ausführbar ist, um mindestens ein Attributvolumen zu generieren, das mindestens ein Attribut umfasst, das aus den seismischen 3D-Daten ableitbar ist.
 
3. Computerimplementierter Algorithmus nach Anspruch 1 oder Anspruch 2, wobei die Bedingung einen selektiv einstellbaren Gewichtungsfaktor enthält.
 
4. Computerimplementierter Algorithmus nach einem der vorangehenden Ansprüche, wobei der Algorithmus ausführbar ist zum:
Propagieren der Grenzfläche in Richtung auf eines der Vielzahl von Kandidatenereignissen innerhalb der vordefinierten Gate-Region und dieses aufnehmend, das ein Akzeptanzkriterium der Wahrscheinlichkeitseigenschaft erfüllt, um eine Fläche entlang der natürlichen Kontur der ersten Region von Interesse zu generieren.
 
5. Computerimplementierter Algorithmus nach einem der vorangehenden Ansprüche, wobei die vordefinierte Gate-Region durch Bedingungen definiert ist, die innerhalb des seismischen 3D-Datenvolumens bereitgestellt sind.
 
6. Computerimplementierter Algorithmus nach einem der vorangehenden Ansprüche, wobei die vordefinierte Gate-Region Ereignisse enthält, die zu unterschiedlichen vertikalen Orten innerhalb des seismischen 3D-Datenvolumens relativ zu der ersten Region von Interesse gehören.
 
7. Computerimplementierter Algorithmus nach einem der vorangehenden Ansprüche, wobei eine Grenzfläche gemäß einem aktiven Konturverfahren und/oder einem Niveaumengen-Verfahren propagiert wird.
 
8. Computerimplementierter Algorithmus nach einem der vorangehenden Ansprüche, wobei der Algorithmus ausführbar ist zum:

(i) Generieren und Zuordnen einer Wahrscheinlichkeitseigenschaft für eine Vielzahl von Kandidatenereignissen innerhalb einer vordefinierten, selektiv einstellbaren Gate-Region, die vor der propagierenden Grenzfläche angeordnet ist;

(ii) Generieren einer Optimierungsfunktion basierend auf der Wahrscheinlichkeitseigenschaft jedes der Vielzahl von Kandidatenereignissen;

(iii) Verformen und Propagieren der Grenzfläche gemäß der Optimierungsfunktion.


 
9. Computerimplementierter Algorithmus nach Anspruch 8, wobei die Optimierungsfunktion eine Kostenfunktion ist, die ausgelegt ist, um einen Kostenwert für jedes der Vielzahl von Kandidatenereignissen innerhalb der vordefinierten Gate-Region zu bestimmen.
 
10. Computerimplementierter Algorithmus nach Anspruch 8, wobei die Optimierungsfunktion ein Kostenfunktionsfeld ist, das ausgelegt ist, um eine externe Kraftfunktion innerhalb der vordefinierten Gate-Region bereitzustellen.
 
11. Verfahren zum adaptiven Bestimmen eines oder mehrerer Horizonte aus seismischen 3D-Daten, umfassend die Schritte:

(a) Generieren mindestens eines Attributvolumens, das eine Vielzahl von seismischen Attributen umfasst, die aus den geologischen Vermessungsdaten bestimmt wurden;

(b) Identifizieren mindestens einer Region von Interesse, die mindestens einen Horizont umfasst, auf einem vorbestimmten Querschnitt des mindestens einen Attributvolumens;

(c) Hinzufügen mindestens eines Seeds zu der mindestens einen Region von Interesse;

(d) Definieren mindestens eines repräsentativen Bereichs gemäß der Region von Interesse;

(e) Generieren eines geologischen Objekts unter Anwendung eines computerimplementierten Algorithmus nach einem der vorangehenden Ansprüche;

(f) Überwachen einer visuellen Darstellung des geologischen Objekts während der Generierung;

(g) selektives Anhalten der Generierung des geologischen Objekts;

(h) Generieren eines optimierten geologischen Objekts durch manuelle und/oder automatische Manipulation mindestens eines Teils des geologischen Objekts gemäß mindestens einer vorbestimmten Bedingung.


 
12. Verfahren nach Anspruch 11, wobei mindestens ein erster repräsentativer Bereich ein Bereich ist, der Teil des mindestens einen Horizonts ist, und mindestens ein zweiter repräsentativer Bereich ein Bereich ist, der nicht Teil des mindestens einen Horizonts ist.
 
13. Verfahren nach einem der Ansprüche 11 und 12, wobei die Schritte (c) bis (e) wiederholt werden, bis ein Akzeptanzkriterium erfüllt ist.
 
14. Verfahren nach einem der Ansprüche 11 bis 13, wobei die Schritte (f) bis (h) wiederholt werden, nachdem mindestens ein zusätzlicher Seed hinzugefügt und/oder mindestens ein zusätzlicher repräsentativer Bereich definiert und/oder das geologische Objekt manuell manipuliert wurde.
 
15. Verfahren nach einem der Ansprüche 11 bis 14, wobei das mindestens eine Attributvolumen eine Vielzahl von Attributvolumen ist, die jeweils aus vorbestimmten Eigenschaftsattributen der geologischen Daten bestimmt werden.
 


Revendications

1. Algorithme mis en œuvre par ordinateur adapté pour propager une surface limite d'une valeur initiale qui est placée à l'intérieur d'une première région d'intérêt d'une représentation visuelle de données sismiques 3D de façon à suivre un contour probable d'une représentation de données non continue d'au moins une partie de ladite première région d'intérêt, ledit algorithme étant exécutable pour :

(i) générer au moins un paramètre de caractéristique pour une pluralité d'événements potentiels desdites données sismiques 3D dans une région de grille prédéfinie située devant ladite surface limite de propagation ;

(ii) générer et attribuer une caractéristique de probabilité pour ladite pluralité d'événements potentiels sur la base dudit au moins un paramètre de caractéristique ;

(iii) déterminer une pluralité d'événements d'au moins une partie d'au moins une seconde région d'intérêt située sensiblement parallèlement à au moins une partie de ladite première région d'intérêt et en conformité avec celle-ci ; et

(iv) propager ladite surface limite à travers ladite représentation de données non continue en utilisant au moins une contrainte reliant ladite surface limite de propagation et ladite pluralité d'événements d'au moins une partie de ladite au moins une seconde région d'intérêt,

ladite au moins une contrainte étant définie conformément auxdites caractéristiques de probabilité attribuées à chacun de ladite pluralité d'événements potentiels d'au moins une partie de ladite première région d'intérêt ; et ladite au moins une contrainte étant en outre adaptée pour fournir une force interne entre des événements respectifs d'au moins une partie de ladite première région d'intérêt et d'au moins une partie de ladite au moins une seconde région d'intérêt ; et ladite force interne entre des événements respectifs étant inversement proportionnelle auxdites caractéristiques de probabilité de chacun de ladite pluralité d'événements d'au moins une partie de ladite première région d'intérêt.
 
2. Algorithme mis en œuvre par ordinateur selon la revendication 1, exécutable en outre pour générer au moins un volume d'attributs comprenant au moins un attribut pouvant être dérivé desdites données sismiques 3D.
 
3. Algorithme mis en œuvre par ordinateur selon la revendication 1 ou la revendication 2, ladite contrainte comprenant un facteur de pondération réglable sélectivement.
 
4. Algorithme mis en œuvre par ordinateur selon l'une quelconque des revendications précédentes, ledit algorithme étant exécutable pour :
propager ladite surface limite vers l'un quelconque de ladite pluralité d'événements potentiels et incorporant celui-ci dans ladite région de grille prédéfinie qui répond à un critère d'acceptation de ladite caractéristique de probabilité de façon à générer une surface le long du contour naturel de ladite première région d'intérêt.
 
5. Algorithme mis en œuvre par ordinateur selon l'une quelconque des revendications précédentes, ladite région de grille prédéfinie étant définie par des contraintes fournies dans ledit volume de données sismiques 3D.
 
6. Algorithme mis en œuvre par ordinateur selon l'une quelconque des revendications précédentes, ladite région de grille prédéfinie comprenant des événements appartenant à différents emplacements verticaux dans ledit volume de données sismiques 3D par rapport à ladite première région d'intérêt.
 
7. Algorithme mis en œuvre par ordinateur selon l'une quelconque des revendications précédentes, une surface limite étant propagée conformément à un procédé de contour actif et/ou un procédé des surfaces de niveau.
 
8. Algorithme mis en œuvre par ordinateur selon l'une quelconque des revendications précédentes, ledit algorithme étant exécutable pour :

(i) générer et attribuer une caractéristique de probabilité pour une pluralité d'événements potentiels à l'intérieur d'une région de grille prédéfinie réglable de manière sélective située devant ladite surface limite de propagation ;

(ii) générer une fonction d'optimisation sur la base de ladite caractéristique de probabilité
de chacun de ladite pluralité d'événements potentiels ;

(iii) déformer et propager ladite surface limite conformément à ladite fonction d'optimisation.


 
9. Algorithme mis en œuvre par ordinateur selon la revendication 8, ladite fonction d'optimisation étant une fonction de coût adaptée pour déterminer une valeur de coût pour chacun de ladite pluralité d'événements potentiels dans ladite région de grille prédéfinie.
 
10. Algorithme mis en œuvre par ordinateur selon la revendication 8, ladite fonction d'optimisation étant un champ de fonction de coût adapté pour fournir une fonction de force externe à l'intérieur de ladite région de grille prédéfinie.
 
11. Procédé permettant la détermination de manière adaptative d'un ou plusieurs horizons à partir de données sismiques 3D, comprenant les étapes de :

(a) génération d'au moins un volume d'attributs comprenant une pluralité d'attributs sismiques déterminés à partir desdites données de prospection géologique ;

(b) identification d'au moins une région d'intérêt, comprenant au moins un horizon, sur une section transversale prédéfinie dudit au moins un volume d'attributs ;

(c) ajout d'au moins une valeur initiale à ladite au moins une région d'intérêt ;

(d) définition d'au moins une zone représentative conformément à ladite région d'intérêt ;

(e) génération d'un objet géologique en appliquant un algorithme mis en œuvre par ordinateur

selon l'une quelconque des revendications précédentes :

(f) surveillance d'une représentation visuelle dudit objet géologique durant la génération ;

(g) arrêt de manière sélective de ladite génération dudit objet géologique ;

(h) génération d'un objet géologique optimisé par manipulation manuelle et/ou automatique d'au moins une partie dudit objet géologique conformément à au moins une contrainte prédéfinie.


 
12. Procédé selon la revendication 11, au moins une première zone représentative étant une zone qui fait partie dudit au moins un horizon et au moins une seconde zone représentative étant une zone qui ne fait pas partie dudit au moins un horizon.
 
13. Procédé selon l'une quelconque des revendications 11 et 12, lesdites étapes (c) à (e) étant répétées jusqu'à ce qu'un critère d'acceptation soit satisfait.
 
14. Procédé selon l'une quelconque des revendications 11 à 13, lesdites étapes (f) à (h) étant répétées après ajout d'au moins une valeur initiale supplémentaire et/ou définition d'au moins une zone représentative supplémentaire et/ou manipulation manuelle de l'objet géologique.
 
15. Procédé selon l'une quelconque des revendications 11 à 14, ledit au moins un volume d'attributs étant une pluralité de volumes d'attributs, chacun déterminé à partir d'attributs de caractéristiques prédéfinis desdites données géologiques.
 




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Cited references

REFERENCES CITED IN THE DESCRIPTION



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Non-patent literature cited in the description